In this second paper of the series, we present the results from optical Gemini-North GMOS-IFU and WIYN DensePak IFU spectroscopic observations of the starburst and inner wind zones of M82, with a focus on the state of the T similar to 10(4) K ionized interstellar medium. Our electron density maps show peaks of a few 1000 cm(-3) (implying very high thermal pressures), local small spatial-scale variations, and a falloff in the minor axis direction. We discuss the implications of these results with regards to the conditions/locations that may favor the escape of individual cluster winds that ultimately power the large-scale superwind. Our findings, when combined with the body of literature built up over the last decade on the state of the interstellar medium (ISM) in M82, imply that the starburst environment is highly fragmented into a range of clouds from small/dense clumps with low-filling factors (< 1 pc, n(e) greater than or similar to 104 cm(-3)) to larger filling factor, less dense gas. The most compact clouds seem to be found in the cores of the star cluster complexes, whereas the cloud sizes in the inter-complex region are larger. These dense clouds are bathed with an intense radiation field and embedded in an extensive high temperature (T greater than or similar to 10(6) K), X-ray-emitting ISM that is a product of the high star formation rates in the starburst zones of M82. The near-constant state of the ionization state of the similar to 10(4) K gas throughout the M82 starburst zone can be explained as a consequence of the small cloud sizes, which allow the gas conditions to respond quickly to any changes. In Paper I, we found that the observed emission lines are composed of multiple components, including a broad (FWHM similar to 150-350 km s(-1)) feature that we associate with emission from turbulent mixing layers on the surfaces of the gas clouds, resulting from the interaction of the fast wind outflows from the synchrotron self-Comptons. The large number of compact clouds and wind sources provides an ideal environment for broad line emission, and explains the large observed broad/narrow-line flux ratios. We have examined in more detail the discrete outflow channel identified within the inner wind in Paper I. The channel appears as a coherent, expanding cylindrical structure of length > 120 pc and width 35 -50 pc. The walls maintain an approximately constant (but subsonic) expansion velocity of similar to 60 km s(-1), and are defined by peaks and troughs in the densities of the different line components. We hypothesize that as the hot wind fluid flows down the channel cavity, it interacts with the cooler, denser walls of the channel and with entrained material within the flow to produce broad-line emission, while the walls themselves emit primarily the narrow lines. We use the channel to examine further the relationship between the narrow and broad component emitting gas within the inner wind. Within the starburst energy injection zone, we find that turbulent motions (as traced by the broad component) appear to play an increasing role with height. Finally, we have argued that a point-like knot identified in GMOS position 4, exhibiting blueshifted (by similar to 140 km s(-1)), broad (less than or similar to 350 km s(-1)) Ha emission and enhanced [S II]/H alpha and [N II]/H alpha ratios, is most likely an ejected luminous blue variable-type object.